Exactness of measured/predicted temperature distributions for heat generation in arbitrary non-variable cross-section bar using entropy generation method

Abstract

• A novel application of second law of thermodynamics. • Usable for validation purposes in every study which involves heat transfer. • Presenting a unique value of non-dimensional total entropy generation rate. • Investigating the effect of cross sectional geometry on lost work. The purpose of the present study is to introduce the entropy generation method as a new validation tool of numerical and experimental studies in the heat transfer field where there exist no similar solutions with which to compare results. Analysis of temperature profiles has been conducted in bars with internal thermal energy generation, constant temperature boundary condition and arbitrary non-variable cross section. The bars have steady state Fourier heat conduction and uniform thermal energy generation. The total rate of entropy generation can be calculated using two different methods: The 1st method is based on integrating local entropy generation rate on the solution domain, and the 2nd one is based on the thermodynamic definition of entropy and the Clausius theorem. The equality of these two results depends on the exactness of the applied temperature profile. The closer the entropy generation rates in the control volume (EGRCVs), the more accurate the predicted temperature profile would be and thus, the obtained results are more reliable. Seven different geometries have been examined for the bar cross section and a correlation between error of temperature distribution and error of entropy generation has been obtained. Moreover, the effect of the cross section geometry on entropy generation has been studied and the distribution of local entropy generation rate for the selected geometries was plotted.